parameter estimates factorial anova

[parisec]

Dear Listers,

This has been bugging me.

I have 2 factors: Factor 1/ treatment (1), control (2);  Factor 2/ low (0), high (1)
Factor 1 is the main variable of interest.

Model 1: Factor 1 only
Model 2: Factor 1 and Factor 2
Model 3: Factor 1, Factor 2, Factor 1 x Factor 2

Results
Model 1: Factor 1 is NS
Model 2: Factor 1 is sig but Factor 2 is not
Model 3: Factor 1 is sig but Factor 2 and interaction are not

I have parameter estimates and means in addition to the anova tables.

For Models 1 and 3, I can derive the means from the parameter estimates and vice versa. But for Model 2, they doesn't jive. I understand that in Model 2, the estimates are corrected for the colinearity between the factors so you can't derive them like in the other 2 models; but where can i find this value of colinearity?

I know why Factor 1 is significant when adjusted for factor 2 based on the distribution of Factor 2 between the levels of Factor 1. But i would like to be able to explain this adjustment numerically instead of the usual "Factor 1 is statistically significant when adjusting for Factor 2".

Is there some way for SPSS to spit these values out so i can validate the parameter estimates with the means? And just why is it that everything jives in Model 3? Is it because it's the saturated model?

Thanks for any light-shedding.
Carol

[Bruce Weaver]

Did you follow this recent thread?

http://spssx-discussion.1045642.n5.nabble.com/Handling-a-Categorical-Covariate-td5724379.html

Are you getting into the same issues discussed there?

parisec wrote

Dear Listers,

This has been bugging me.

I have 2 factors: Factor 1/ treatment (1), control (2);  Factor 2/ low (0), high (1)
Factor 1 is the main variable of interest.

Model 1: Factor 1 only
Model 2: Factor 1 and Factor 2
Model 3: Factor 1, Factor 2, Factor 1 x Factor 2

Results
Model 1: Factor 1 is NS
Model 2: Factor 1 is sig but Factor 2 is not
Model 3: Factor 1 is sig but Factor 2 and interaction are not

I have parameter estimates and means in addition to the anova tables.

For Models 1 and 3, I can derive the means from the parameter estimates and vice versa. But for Model 2, they doesn't jive. I understand that in Model 2, the estimates are corrected for the colinearity between the factors so you can't derive them like in the other 2 models; but where can i find this value of colinearity?

I know why Factor 1 is significant when adjusted for factor 2 based on the distribution of Factor 2 between the levels of Factor 1. But i would like to be able to explain this adjustment numerically instead of the usual "Factor 1 is statistically significant when adjusting for Factor 2".

Is there some way for SPSS to spit these values out so i can validate the parameter estimates with the means? And just why is it that everything jives in Model 3? Is it because it's the saturated model?

Thanks for any light-shedding.
Carol

[parisec]

No...I haven't. I searched "parameter estimates factorial anova". i'll check that out.

thanks!

[parisec]

After reading through the thread, it looks like i'm bugged about something different. I used Art's suggestion of including my bivariate "covariate" as a factor in a 2x2 anova.

I'm trying to make sense of the Intercept and the factor A and B parameter estimates of the main effects model.

For Model 1 -unadjusted, and Model 3 - main effects + interaction, these estimates can be derived by the means. For example in the unadjusted model, the intercept is the mean of the control, for the model with the interaction, the intercept is the mean of control+high...but for the life of me, i can't figure out what the intercept in my main effects model represents.

I came across this article which talks about differences between using effect coding and dummy coding.  

http://psych.unl.edu/psycrs/971/factorial/fact_reminder.pdf

...which is the closest thing i can find that comes out and says: "the regression weights don't reflect the main effect marginal mean differences because the parameters correct for the  colinearity amongst the effects".

But I'd like to be able to visibly show how those estimates in the main effects model are based off of the means. So i'm wondering if there is a way to see what the colinearity is that is being corrected for.

Is this possible?

[Bruce Weaver]

For your Model 2, include this EMMEANS sub-command (and YES, I do know you don't include the A*B interaction in Model 2):

  /EMMEANS=TABLES(A*B)

Then use information from the table of parameter estimates to compute those 4 cell means as follows:

1) Constant
2) Constant + coefficient for A
3) Constant + coefficient for B
4) Constant + coefficient for A + coefficient for B

Here's an example using the Survey_sample.sav file that comes with SPSS.

NEW FILE.
DATASET CLOSE all.

GET FILE='C:\SPSSdata\Survey_sample.sav'.

COMPUTE WhiteRace = race EQ 1.
COMPUTE Male = sex EQ 1.
COMPUTE Female = sex EQ 2.
FORMATS WhiteRace Male Female(f1).
CROSSTABS Male Female by WhiteRace.

* Model 1: Factor 1 (Male) only.

UNIANOVA age BY Male
  /METHOD=SSTYPE(3)
  /EMMEANS=TABLES(Male) COMPARE
  /PRINT=parameter
  /DESIGN=Male.

* Model 2: Factor 1 and Factor 2, no interaction.

UNIANOVA age BY Male WhiteRace
  /METHOD=SSTYPE(3)
  /EMMEANS=TABLES(Male) COMPARE
  /EMMEANS=TABLES(WhiteRace) COMPARE
  /EMMEANS=TABLES(Male*WhiteRace)
  /PRINT=parameter
  /DESIGN=Male WhiteRace.

* To get the 4 cell means from the last EMMEANS table:
* 1) Constant
* 2) Constant + coefficient for Male
* 3) Constant + coefficient for WhiteRace
* 4) Constant + coefficient for Male + Coefficient for WhiteRace.

OUTPUT:

Means from EMMEANS table:

Male WhiteRace Mean
               
0 0 41.392
        1 47.752
1 0 39.388
        1 45.748

Means from computations shown above:

M W Mean
1 1 45.748
0 1 47.752
1 0 39.388
0 0 41.392

HTH.

parisec wrote

After reading through the thread, it looks like i'm bugged about something different. I used Art's suggestion of including my bivariate "covariate" as a factor in a 2x2 anova.

I'm trying to make sense of the Intercept and the factor A and B parameter estimates of the main effects model.

For Model 1 -unadjusted, and Model 3 - main effects + interaction, these estimates can be derived by the means. For example in the unadjusted model, the intercept is the mean of the control, for the model with the interaction, the intercept is the mean of control+high...but for the life of me, i can't figure out what the intercept in my main effects model represents.

I came across this article which talks about differences between using effect coding and dummy coding.  

http://psych.unl.edu/psycrs/971/factorial/fact_reminder.pdf

...which is the closest thing i can find that comes out and says: "the regression weights don't reflect the main effect marginal mean differences because the parameters correct for the  colinearity amongst the effects".

But I'd like to be able to visibly show how those estimates in the main effects model are based off of the means. So i'm wondering if there is a way to see what the colinearity is that is being corrected for.

Is this possible?

[parisec]

Thanks Bruce. I'll give it a shot and report back.

[Richard Ristow]

At 01:47 PM 3/12/2014, parisec wrote:

>I have 2 factors:
>Factor 1/ treatment (1), control (2);
>Factor 2/ low (0), high (1)
>Factor 1 is the main variable of interest.
>
>Model 1: Factor 1 only
>Model 2: Factor 1 and Factor 2
>Model 3: Factor 1, Factor 2, Factor 1 x Factor 2
>
>Results
>Model 1: Factor 1 is NS
>Model 2: Factor 1 is sig but Factor 2 is not
>Model 3: Factor 1 is sig but Factor 2 and interaction are not

Do you have a balanced design, with the same proportions of low and
high on Factor 2, within your two treatment groups? Otherwise, in
regression terms, your inputs are correlated, and including/excluding
one variable can effect the parameter values and significance test
for the other.

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD

[parisec]

Hi Richard,

No, the design is not balanced. There are more cases of Factor 2=High in Factor 1=Treatment. I know that the reason that my main effects model is significant but the unadjusted model is not is that factor A and factor B are correlated. What i want to see is the numeric value of the correlation. I ran my analysis using /EMEANS compare that Bruce suggested but have not had a chance to dig into the results of my output yet or run the sample commans he posted.

Carol

-----Original Message-----
From: Richard Ristow [mailto:[hidden email]]
Sent: Friday, March 14, 2014 11:07 AM
To: Parise, Carol A.; [hidden email]
Subject: Re: parameter estimates factorial anova

At 01:47 PM 3/12/2014, parisec wrote:

>I have 2 factors:
>Factor 1/ treatment (1), control (2);
>Factor 2/ low (0), high (1)
>Factor 1 is the main variable of interest.
>
>Model 1: Factor 1 only
>Model 2: Factor 1 and Factor 2
>Model 3: Factor 1, Factor 2, Factor 1 x Factor 2
>
>Results
>Model 1: Factor 1 is NS
>Model 2: Factor 1 is sig but Factor 2 is not Model 3: Factor 1 is sig
>but Factor 2 and interaction are not

Do you have a balanced design, with the same proportions of low and high on Factor 2, within your two treatment groups? Otherwise, in regression terms, your inputs are correlated, and including/excluding one variable can effect the parameter values and significance test for the other.

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD